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Annuary Calendar
The '''Annuary Calendar' is a Calendar invented by in which each year has twelve regular months alternating between 29 and 30 days plus a 30-day intercalary month occurring once every 33 months.'' Such a calendar has an 8-year cycle of 99 months with a mean year of 365.25 days. To reduce the mean year to 365.2425 days three intercalary months every 400 years have 29 days (instead of 30 days). The mean month is a little short of a lunar month and the calendar has a rule to reckon the slow drift of the moon phases against the calendar month. ''Introduction'' Some time ago I invented a solar calendar in which the months are approximately lunar. In this calendar a year has 12 months alternating between 29 and 30 days. To these is added an intercalary month of 30 days once every 32 ordinary months before a month of 29 days. The calendar as such has an 8 year cycle of 2922 days, giving an average year of 365.25 day (same as Julian Calendar). The month runs about 1 1/2 days short of a lunar month each 8 year cycle (i.e. 1/2 day short per intercalary month). Because every 33rd month is intercalary, I call it the IC33 calendar. The year can be made more accurate by shortening one intercalary month every 128 years to 29 days (Mean Tropical Year) IC33-128 or 3 intercalary months every 400 years IC33-400 (Gregorian year) Tracking the Drift of the Moonphase Around August 1998 discovered a simple way of tracking the slow drift of the lunar month against this calendar month, which works for any variety of year. For each month I define a lunar index that changes infrequently. It can take any value from 1.0 to 29.5 in whole or half numbers. If it's a whole number, the new moon is reckoned to be on that day of the month, else you round down for 29 day months and up for 30 day months. The lunar index changes exactly halfway between two intercalations (to effect the 17th month after) and immediately before and after a 29 day intercalary month. The change is an increase of 0.5, except in the case were the lunar index is already 29.5. Then it changes to 1.0 and the first month with 1.0 (which has 29 days) has no new moon day, because the previous month has one at the end. So the lunar index cycles through 58 values before returning to its original value and one month misses a new moon day in each such cycle. The Months The months are named thus. Annuary, Bebry, Carch, Daipril, (Eapril), Fay, Gyne, Huly, Igust, (Jawgust), Keptember, Luctober, Myvember, Nicember, (Ocember). Eapril, Jawgust and Ocember are intercalary months. Each one occurs once every 8 years. The Month Start Dates Except between the end of a 29 day intercalary month and a dropped leap-day, all months start on the following Gregorian dates: Annuary Calendar Month Start dates (position corresponding to name as shown above) Remainder 0: (e.g. 4800 begins 30 Dec 1999) 30 Dec 28 Jan 27 Feb 27 Mar 26 Apr 25 May 24 Jun 23 Jul 22 Aug 20 Sep 20 Oct 18 Nov 18 Dec Remainder 1: (e.g. 4801 begins 17 Jan 2001) 17 Jan 15 Feb 17 Mar 15 Apr 15 May 13 Jun 13 Jul 11 Aug 10 Sep 09 Oct 08 Nov 07 Dec Remainder 2: (e.g. 4802 begins 6 Jan 2002) 06 Jan 04 Feb 06 Mar 04 Apr 04 May 02 Jun 02 Jul 31 Jul 30 Aug 28 Sep 28 Oct 26 Nov Remainder 3: (e.g. 4803 begins 26 Dec 2002). 26 Dec 24 Jan 23 Feb 24 Mar 23 Apr 22 May 21 Jun 20 Jul 19 Aug 18 Sep 17 Oct 16 Nov 15 Dec Remainder 4: (e.g. 4804 begins 14 Jan 2004) 14 Jan 12 Feb 13 Mar 11 Apr 11 May 09 Jun 09 Jul 07 Aug 06 Sep 05 Oct 04 Nov 03 Dec Remainder 5: (e.g. 4805 begins 2 Jan 2005) 02 Jan 31 Jan 02 Mar 31 Mar 30 Apr 29 May 28 Jun 27 Jul 26 Aug 24 Sep 24 Oct 22 Nov Remainder 6: (e.g. 4806 begins 22 Dec 2005) 22 Dec 20 Jan 19 Feb 20 Mar 19 Apr 19 May 17 Jun 17 Jul 15 Aug 14 Sep 13 Oct 12 Nov 11 Dec Remainder 7: (e.g. 4807 begins 10 Jan 2007) 10 Jan 08 Feb 10 Mar 08 Apr 08 May 06 Jun 06 Jul 04 Aug 03 Sep 02 Oct 01 Nov 30 Nov The New Moon Days of Months The lunar index for Annuary 4805 (2 Jan 2005) to Igust 4807 (2 Sept 2007) inclusive is 10.0 so all those months have a new moon day on the 10th. After that for the next 33 months, the lunar index is 10.5 so the new moon day is the 10th day of the 29 day months and the 11th day of the 30 day months. The Lunar indices and new moon days for years 4789 to 4820 (1989-01-02 to 2021-01-01 AD) inclusive are: Annuary Range Gregorian Range Index 29dm 30dm 4789A to 4791I 1989-01-02 to 1991-09-02 7.0 7 7 4791K to 4794D 1991-09-03 to 1994-05-03 7.5 7 8 4794F to 4796N 1994-05-04 to 1997-01-01 8.0 8 8 4797A to 4799I 1997-01-02 to 1999-09-02 8.5 8 9 4799K to 4802D 1999-09-03 to 2002-05-03 9.0 9 9 4802F to 4804N 2002-05-04 to 2005-01-01 9.5 9 10 4805A to 4807I 2005-01-02 to 2007-09-02 10.0 10 10 4807K to 4810D 2007-09-03 to 2010-05-03 10.5 10 11 4810F to 4812N 2010-05-04 to 2013-01-01 11.0 11 11 4813A to 4815I 2013-01-02 to 2015-09-02 11.5 11 12 4815K to 4818D 2015-09-03 to 2018-05-03 12.0 12 12 4818F to 4820N 2018-05-04 to 2021-01-01 12.5 12 13 The dark moon (astronomical new moon) will usually occur on the new moon day or the previous day. For example, the eclipse of 11 August 1999 occurred on 8 Igust 4799 (day before new moon day) and the eclipse of 29 March 2006 occurred on 10 Daipril 4806 (a new moon day). Most months in my Yerm calendar begin on the new moon day, but when the lunar index is higher, more (but still a minority) will begin the next day. I've also defined a lunar index for the full moon, which progresses in the same way as the lunar index for the new moon and is either 14 greater or 15 less than the new moon lunar index. The Solar Days of Months Because a year may have either 12 or 13 months, a given month may move around up to a month relative to the seasons. To enable a more accurate scheduling relative to the seasons, each non-intercalary month has a solarday. The month after an intercalary month has its first day as a solar day, then each month has its solar day one day later. Because there are 32 rather than 30 months between each successive pair of intercalary months, there are two occasions when this progression of the solar day is halted. These are the nineth month after the intercalary month (solar day halts at 8) and the twenty fifthmonth after the intercalary month (solar day halts at 23). Over the 8-year cycle the solar day of each month is: Month Year of 8-year Cycle 0 1 2 3 4 5 6 7 Annuary 20 1 12 23 5 16 27 8 Bebry 21 2 13 24 6 17 28 9 Carch 22 3 14 25 7 18 29 10 Daipril 23 4 15 26 8 19 30 11 Eapril XX Fay 23 5 16 27 8 20 1 12 Gyne 24 6 17 28 9 21 2 13 Huly 25 7 18 29 10 22 3 14 Igust 26 8 19 30 11 23 4 15 Jawgust XX Keptember 27 8 20 1 12 23 5 16 Luctober 28 9 21 2 13 24 6 17 Myvember 29 10 22 3 14 25 7 18 Nicember 30 11 23 4 15 26 8 19 Ocember XX NB: The intercalary months (marked XX) have no solar day. The solar days are not only useful for tracking the seasons, but also for reckoning the insertion intercalary months (after a solar day on the 30th). Also the halfway point when the lunar index is changes is when the solar day changes from 15 to 16. Long Term Accuracy The new and full moon days repeat once every 11600 years, giving a mean period of 29.530591 days. The 11600 years is the absolute cycle of this ONE DAY BEFORE calendar, the 725-years cycle is relative to the Gregorian calendar. The Seven Day Week The 33 month cycle of this calendar has one day more than a whole number of weeks, except when the intercalary month is shortened, then it has a whole number of weeks. So 1 Annuary 4805 was Sunday 2 January 2006 and 33 months later 1 Keptember 4807 will be Monday 3 September 2007. External Link Annuary Calendar Category:Proposed calendars Category:400-year leap cycle Category:Radical designs Category:12+1 Category:29:30 Category:Karl Palmen